Computation of time optimal control problems governed by linear ordinary differential equations
type: Item
instance of: scholarly article
title: Computation of time optimal control problems governed by linear ordinary differential equations
zbMATH Open document ID: 1382.65185
author: Xiliang Lu
author: Lijuan Wang
author: Qishu Yan
published in: Journal of Scientific Computing
publication date: 2017-12-14T00:00:00Z
review text: The computation of the optimal time for a time optimal control problem governed by a system of linear ordinary differential equations is approached by transforming the problem into an equivalent norm optimal control problem. Properties of the two problems are extensively studied: bang-bang type principle, equivalence property, first-order necessary and sufficient condition. A bisection based root finding algorithm to compute the optimal time is elaborated by solving a sequence of norm optimal control problems and their Lagrangian dual problems. The convergence of the optimal norm is proved. An iteratively reweighted least squares method is described in order to solve the nonsmooth Lagrangian dual optimization problem. The efficiency of the proposed numerical algorithm is shown by means of a few practical examples.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49M30
zbMATH DE Number: 6818457
zbMATH Keywords: time optimal control
zbMATH Keywords: norm optimal control
zbMATH Keywords: ordinary differential equation
zbMATH Keywords: bisection method
zbMATH Keywords: iteratively reweighted least squares
zbMATH Keywords: numerical example
zbMATH Keywords: bang-bang type principle
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: s10915-017-0403-1
OpenAlex ID: W2592416073
cites work: Analysis and control of nonlinear infinite dimensional systems
cites work: Smoothing methods for nonsmooth, nonconvex minimization
cites work: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
cites work: Iteratively reweighted least squares minimization for sparse recovery
cites work: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
cites work: Q5311330
cites work: Functional analysis and time optimal control
cites work: The Primal-Dual Active Set Strategy as a Semismooth Newton Method
cites work: Semismooth Newton Methods for Time-Optimal Control for a Class of ODEs
cites work: Computations and time-optimal controls
cites work: Computational method for time-optimal switching control
cites work: Time optimal control of the heat equation with pointwise control constraints
cites work: Q3273446
cites work: Efficient algorithm for time-optimal control of a two-link manipulator
cites work: Q3285814
cites work: Q4486034
cites work: Q4400449
cites work: An approach to the optimal time for a time optimal control problem of an internally controlled heat equation
cites work: On the Equivalence of Minimal Time and Minimal Norm Controls for Internally Controlled Heat Equations
cites work: The time optimal control with constraints of the rectangular type for linear time-varying ODEs
cites work: Q5188502
DOI: 10.1007/S10915-017-0403-1
description: scientific article; zbMATH DE number 6818457